Prove that: (a=alpha)Tan a +2tan 2a+ 2^2tan2^2a +....................... 2^n-1tan2^n-1a + 2^ncot2^n a = cot a

Question

Akash Ojha · Answer

We know, cotA - tanA = 2cot2A=> tanA = cotA - 2cot2AHence, the above series can be rewritten as:-(cotA - 2cot2A) + 2(cot2A - 2cot4A) + 2^2(cot4A - 2cot8A) + ........+ 2^n-1(cot2^n-1A - 2cot2^nA) + 2^ncot2^nA= cotA(Since all the rest terms cancel each other out except first term cotA)

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Prove that: (a=alpha)Tan a +2tan 2a+ 2^2tan2^2a +....................... 2^n-1tan2^n-1a + 2^ncot2^n a = cot a

Prove that: (a=alpha)Tan a +2tan 2a+ 2^2tan2^2a +....................... 2^n-1tan2^n-1a + 2^ncot2^n a = cot a

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Prove that: (a=alpha)Tan a +2tan 2a+ 2^2tan2^2a +....................... 2^n-1tan2^n-1a + 2^ncot2^n a = cot a

Prove that: (a=alpha)Tan a +2tan 2a+ 2^2tan2^2a +....................... 2^n-1tan2^n-1a + 2^ncot2^n a = cot a

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